Showing papers in "Numerical Heat Transfer Part A-applications in 1991"
TL;DR: In this article, the mixed convection transport from an isolated thermal source, with a uniform surface heat flux input and located in a rectangular enclosure, is studied numerically, where an airstream flows through the openings on the two vertical walls.
Abstract: The mixed convection transport from an isolated thermal source, with a uniform surface heat flux input and located in a rectangular enclosure, is studied numerically. The enclosure simulates a practical system such as an oven or an air-cooled electronic device, where an airstream flows through the openings on the two vertical walls. The heat source represents a heater or an electronic component located in such an enclosure. The interaction of the cooling stream with the buoyancy-induced flow from the heat source is of interest in this work. Laminar, two-dimensional flow is assumed, and the problem lies in the mixed convection regime, governed by the buoyancy parameter GrIRe1 and the Reynolds number Re. Other significant variables include the locations of the heat source and the outflow opening. The inflow is kept at a fixed position. The mathematical model is developed with vorticity and stream function, along with temperature, as the dependent variables. The unsteady terms are retained in the vo...
125 citations
TL;DR: In this article, a complete mathematical model for transient two-dimensional heat pipes is presented and the numerical results for both simulated compressible vapor flow with high Mach numbers and the vapor flow of a high-temperature heat pipe are compared with the experimental data in the literature.
Abstract: A complete mathematical model for transient two-dimensional heat pipes is presented. The numerical results for both simulated compressible vapor flow with high Mach numbers and the vapor flow of a high-temperature heat pipe are compared with the experimental data in the literature. The transient responses of heat pipes to a pulsed heat input are also investigated. It is very important to include the porous wick and the wall in the numerical calculations for the transient analysis of heat pipes and to treat the entire heat pipe as a single system rather than to analyze the vapor flow alone.
119 citations
TL;DR: In this paper, a direct integration method is developed for determining good initial guesses for the unknown property coefficients within about 10% error, and the Levenberg-Marquardt method is then applied to refine the results to within a specified convergence criterion.
Abstract: One of the difficulties in the solution of inverse heat conduction problems is that of making sufficiently accurate initial guesses for the unknowns in order to start the iterations. In this work a direct integration method is developed for determining good initial guesses for the unknown property coefficients within about 10% error. The Levenberg-Marquardt method is then applied to refine the results to within a specified convergence criterion. The problem studied here is concerned with simultaneous estimation of temperature dependent thermal conductivity and heat capacity from the multiple spatial and temporal measurements taken during transient heat conduction. Interior temperature sensors are found to be necessary when the properties vary with respect to temperature. A statistical analysis is performed to determine approximate confidence bounds for estimating the thermal conductivity and heal capacity per unit volume
92 citations
TL;DR: In this article, the phenomenon of natural convection in a square enclosure heated and cooled in the horizontal direction was investigated numerically in the Prandtl number range 0.01-10 and the Rayleigh number range 102-1011.
Abstract: The phenomenon of natural convection in a square enclosure heated and cooled in the horizontal direction was investigated numerically in the Prandtl number range 0.01-10 and the Rayleigh number range 102-1011. The numerical method relied on the full governing equations for time-dependent flows. The study focused on the detection of inertia-sustained fluctuations in the flow field and on the highest Rayleigh number where steady-state laminar flows are possible. It was found that the highest Rayleigh number decreases dramatically as the Prandtl number decreases. This finding agrees qualitatively with experimental observations of transition to turbulent natural convection and with the “local Reynolds number” criterion of transition to turbulence recommended by the buckling theory of turbulent flow.
77 citations
TL;DR: In this paper, a finite difference computer code incorporating two methods of discretization for the advection terms in the flow governing conservation equations has been developed, and application of the code to a stratified thermal storage showed very good agreement between the experimental and the predicted temperature profiles.
Abstract: A finite difference computer code incorporating two methods of discretization for the advection terms in the flow governing conservation equations has been developed. These methods are the weighted upwind difference scheme (WUDS) and the second-order upwind difference scheme (SOUDS). Application of the code to a stratified thermal storage showed very good agreement between the experimental and the predicted temperature profiles when using SOUDS as opposed to WUDS. Investigation of the effect of inlet geometry on thermal stratification in a thermal storage tank was carried out using the SOUDS method. Results show that the effect of inlet geometry is negligible for Richardson numbers above 10. Thus a performance criterion for stratified thermal storage tanks with different inlet geometries has been established.
62 citations
TL;DR: In this paper, the effect of buoyancy on the flow and heat transfer between a horizontal cold surface and an infinite two-dimensional array of open cavities heated from below is studied numerically.
Abstract: The effect of buoyancy on the flow and heat transfer that develop between a horizontal cold surface and an infinite two-dimensional array of open cavities heated from below is studied numerically. In earlier investigations the steady-state features of this problem were studied for the case of unbounded flow above the cavities. The resulting flow pattern was found to be symmetrical with respect to the centerlines of the cavities. In the present work it is shown that the symmetry of the flow can be destroyed due to the presence of an upper wall. The evolutionary path to steady-state flow is examined, and sustained oscillatory behavior has been observed in several cases. The solution structure is governed by five parameters, i.e., the geometric parameters A = l'/H', B = h'/H', and C = L'/H', the Rayleigh number Ra = gβ ΔT' H' 3/av, and the Prandtl number Pr = v/α. For a geometry with A = ½z, B = ¼, and C = 1, a complicated solution structure is observed upon increasing the Rayleigh number. For Ra ≤ ...
56 citations
TL;DR: In this paper, numerical solutions based on the streamfunction-vorticity formulation were obtained for two-dimensional flow of air in a differentially heated, slender cavity with conducting fins on the cold wall, for Rayleigh numbers of 103-105, angles of inclination of 45° and 90°, overall aspect ratios of 20 and ∞, and microcavity aspect ratios (A) of 20-0.25.
Abstract: Numerical solutions, based on the streamfunction-vorticity formulation, were obtained for two-dimensional flow of air in a differentially heated, slender cavity with conducting fins on the cold wall, for Rayleigh numbers of 103-105, angles of inclination of 45° and 90°, overall aspect ratios of 20 and ∞, and microcavity aspect ratios (A) of 20-0.25. As A was decreased from a value of 20, the flow pattern evolved as follows: a primary circulation state, a boundary layer regime with recirculations and decreasing primary circulation, an increase in primary circulation, a separation of the recirculating stream from the interfin space, and a final state of primary circulation restricted to the unfinned side. The average Nusselt number at a given fin length also evolved during these transitions, showing maximum and minimum values whose locations depended only on Ra. Limited results showing the dependence of flow and heat transfer variables on dimension-less fin length are also given. A series of recommendations...
56 citations
TL;DR: In this article, the authors investigate the flow pattern and forced convective heat transfer in supercritical flows, such as those encountered in compact heat exchangers, and show that these flows exhibit laminar self-sustained oscillations at the plane channel Tollmien-Schlichting frequency for Reynolds numbers above the critical one.
Abstract: Numerical investigations of the flow pattern and forced convective heat transfer in supercritical flows, such as those encountered in compact heat exchangers, are presented. These flows exhibit laminar self-sustained oscillations at the plane channel Tollmien-Schlichting frequency for Reynolds numbers above the critical one. These studies indicate that oscillatory separated flow results in large-scale convective patterns that are responsible for significant heat transfer enhancement and leads to a reduction in the pumping power required to achieve a given Nusselt number. The hydrodynamic-heat transfer numerical results are obtained by direct simulation of the unsteady energy and Navier-Stokes equations using a spectral element method for the spatial discretization. The spectral element method is a high-order weighted-residual technique that exploits both the common features and the competitive advantages of low-order finite element methods (versatility) and spectral techniques (accuracy and rapid converge...
51 citations
TL;DR: In this paper, the authors performed numerical experiments on an incompressible fluid contained in a tilted nonrectangular enclosure and found that the heat transfer and fluid motion within the enclosure are strong functions of Rayleigh number, Prandtl number, and orientation angle of the enclosure.
Abstract: Numerical experiments were performed on an incompressible fluid contained in a tilted nonrectangular enclosure. Rayleigh numbers of l02-l05 and Prandtl numbers of 0.001-100 are considered. The wall angles are 22.5°, 45°, and 77.5° with aspect ratios of 3 and 6. Results indicate that the heat transfer and fluid motion within the enclosure are strong functions of Rayleigh number, Prandtl number, and orientation angle of the enclosure. For Rayleigh numbers greater than 1& and Prandtl numbers greater than 0.1, a minimum and a maximum mean Nusselt number occurred as the angle of orientation was increased from 0° to 360°. A transition in the mode of circulation occurred at the angles corresponding to the minimum or maximum rate of heat transfer.
47 citations
TL;DR: In this article, numerical solutions for the fluid flow in a heat exchanger consisting of an array of diamond-shaped pin fins were obtained for the periodic fully developed regime, whereby the velocity field repeats itself from row to row and the pressure field also repeats periodically relative to a linear axial decrease.
Abstract: Numerical solutions were obtained for the fluid flow in a heat exchanger consisting of an array of diamond-shaped pin fins. The model that underlies the solutions is based on the concept of the periodic fully developed regime, whereby the velocity field repeats itself from row to row and the pressure field also repeats periodically relative to a linear axial decrease. Implementation of the model was accomplished via the finite element method, whereby the solution domain was discretized by subdividing it into an assemblage of two-dimensional, nine-noded quadrilateral elements. As a prelude to the final numerical solutions, a systematic study was performed to establish the number of elements needed for the attainment of accurate results. For validation purposes, solutions were run for arrays of circular cylindrical pin fins (i.e., tube banks) and specific arrays of diamond-shaped pin fins to enable comparisons of pressure drop predictions with available experimental data. The final set of numerical solution...
42 citations
TL;DR: In this article, a pure numerical method is proposed for solving the solidification temperature, solid fraction, and liquid composition correlation (T-fs-CL) in strongly coupled binary solidification problems.
Abstract: A pure numerical method is proposed for solving the solidification temperature, solid fraction, and liquid composition correlation (T-fs-CL) in strongly coupled binary solidification problems. The method accommodates both single-phase and eutectic solidification processes and eliminates the need to assume any specified function for the local T-fs-CL relationship or the linearizations of the liquidus and solidus for a given alloy. A sample calculation performed with an Al-4.5%Cu alloy, a hypoeutectic system, illustrates the feasibility of the established numerical method. Further discussion shows that the proposed numerical solution to the T-fs-CL coupling will also be suitable for local remelting simulations.
TL;DR: In this article, a row of in-line cylinders placed between two parallel plates are studied numerically, and heat transfer and fluid flow over the row of cylinders are studied. But the authors focus on the separation of flow in the separated zone.
Abstract: Heat transfer and fluid flow over a row of in-line cylinders placed between two parallel plates are studied numerically. Flow is incompressible, two-dimensional, and laminar. The spacing between cylinders causes three different separation patterns. When the spacing is small, the separated flow between cylinders is stable. As the spacing increases, flow in the separated zone becomes temporal and periodic. At higher spacing, the separated flow is local and does not extend to the next cylinder. In general, the pressure drop in the flow and heat transfer to the flow are spatially periodic, indicating fully developed characteristics
TL;DR: In this paper, the Navier-Stokes and energy equations for laminar flow in a horizontal channel with localized heating from below were numerically solved for a wide range of Rayleigh Ra, Reynolds Re, and Prandtl Pr numbers.
Abstract: Two-dimensional Navier-Stokes and energy equations are numerically solved for laminar flow in a horizontal channel with localized heating from below. The relative strength of the forced flow and buoyancy effects are examined for a wide range of Rayleigh Ra, Reynolds Re, and Prandtl Pr numbers. For a fixed geometry and a given Rayleigh number, a complicated solution structure is observed upon increasing the Reynolds number. For Re = 0 (i.e., in the case of pure free convection), a steady symmetric flow pattern is obtained. This pattern becomes asymmetric for Re below a critical value, but the rolls remain attached to the heating elements. Above the critical Re, the rolls are carried downstream with a time-dependent velocity, and the flow becomes periodic in time.
TL;DR: In this paper, a basic variable, explicit finite difference scheme is used to solve the unsteady and strongly pressure-coupled velocity problems of liquid flows induced both by thermosolutal buoyancies and solidification shrinkage in a binary alloy solidification process.
Abstract: A basic-variable, explicit finite difference scheme is used to solve the unsteady and strongly pressure-coupled velocity problems of liquid flows induced both by thermosolutal buoyancies and solidification shrinkage in a binary alloy solidification process. A sample calculation, performed on an IBM personal computer, for a horizontally solidified Al-4.5%Cu alloy in a high-H/L ratio cavity with a top riser shows that the shrinkage established pressure gradient in the mushy region can be several hundred, even several thousand, times larger than that in the bulk liquid region.
TL;DR: In this paper, the authors analyzed the effect of lid shear on convective motion and heat transfer in a square cavity driven by combined temperature gradient and imposed lid-shear, and the evolution of unsteady flow in a cavity is discussed.
Abstract: Transient convective motion and heat transfer in a square cavity driven by combined temperature gradient and imposed lid shear are analyzed. The cavity is filled with a low Prandtl fluid, and the vertical walls are maintained at different but constant temperatures. The horizontal connecting walls are adiabatic. The upper wall is moving and either aids or opposes the buoyancy-driven motion. A control volume method is employed to compute the flow and temperature fields. Numerical results are reported for Pr = 0·005, Gr = 1 × I07, and a range of Reynolds numbers for both aiding and opposing flow situations. The evolution of unsteady flow in a cavity is discussed. For GrIRe2 ≥ 1 the effect of inertia is insignificant. For GrIRe2 ≤ 1 the inertia stabilizes the flow, regardless of the direction of the applied shear force.
TL;DR: In this paper, the authors presented heat transfer data for laminar incompressible flow over a row of in-line cylinders between two parallel plates, where the cylinder and plate temperatures were assumed to be constant but not necessarily the same.
Abstract: Numerically calculated heat transfer data are presented for laminar incompressible flow over a row of in-line cylinders between two parallel plates. The cylinder and plate temperatures are assumed to be constant but not necessarily the same. The spacing between cylinders changes the flow in the separated zone and subsequently affects the heat transfer. The heat transfer data for different aspect ratios and Reynolds numbers are reduced to form a single formula for ease of interpolation. The method of calculating overall heat transfer from multiple cylinder-plate modules is studied, and working relations are obtained
TL;DR: In this paper, a three-dimensional numerical study was performed on interactions of natural convection and radiation in a cubical enclosure filled with carbon dioxide gas, where the enclosure was heated differentially by two opposing vertical walls, and the mean heat transfer correlation was proposed as Nu = 0·323 Ra0·342 in the surface/gas radiation mode, where Nu is the time and spatially averaged Nusselt number at the isothermal walls.
Abstract: A three-dimensional numerical study was performed on interactions of natural convection and radiation in a cubical enclosure filled with carbon dioxide gas. The enclosure was heated differentially by two opposing vertical walls. Gas radiation was analyzed by the P1 differential approximation method and the weighted sum of gray gas model. Computations were carried out over a range of the Rayleigh number, Ra, between 105 and 109. The Prandtl number and the overheat ratio were held fixed at 0·68 and 1·0, respectively. Unsteady transitional flows were computed by a direct simulation method, without using any explicit turbulence models. From the predictions, a mean heat transfer correlation has been proposed as Nu = 0·323 Ra0·342 in the surface/gas radiation mode, where Nu is the time and spatially averaged Nusselt number at the isothermal walls.
TL;DR: In this paper, a boundary integral equation method has been developed to analyze surface temperatures generated by friction in sliding contact, which can handle any combination of finite or semi-infinite geometry, thermal properties, sliding velocity, and multiple, interacting contact areas.
Abstract: A boundary integral equation method has been developed to analyze surface temperatures generated by friction in sliding contact. Surface temperature is an important factor in tribology. The method readily handles any combination of finite or semi-infinite geometry, thermal properties, sliding velocity, and multiple, interacting contact areas. In order to handle the sliding velocity, a moving Green's function is used, which incorporates the convective effect of the motion in a convenient and accurate manner. Numerical studies show that the method is unconditionally stable using a midpoint rule to handle the numerical integrations. Relatively large time steps and large boundary elements can be used to obtain converged and accurate results. Also, the general three-dimensional regions require discretisation only over two-dimensional surfaces. Overall, these factors lead to a solution method that is computationally efficient and accurate. Results show that the Piclet number, the sliding velocity, and ...
TL;DR: In this paper, the numerical prediction of laminar natural convection in two-dimensional enclosures with inner bodies of irregular but basically cylindrical shape is the subject of this paper.
Abstract: The numerical prediction of laminar natural convection in two-dimensional enclosures with inner bodies of irregular but basically cylindrical shape is the subject of this paper. This problem models, for example, the fluid dynamics in a nuclear spent-fuel storage container in which the inner body represents a tight water or a fast breeder reactor fuel assembly The solution method described employs a nonorthogonal coordinate system in which the surfaces of the inner and outer boundaries coincide with coordinate surfaces. The coordinate system is generated with simple algebraic expressions. The transformed equations of motion and energy are derived on a control volume basis with central and upwind finite differences. Details of the derivation are provided. The discretiigd equations are solved within the framework of the Simplest scheme for orthogonal systems. Application of the solution methodology is illustrated with three examples.
TL;DR: In this article, the authors compared the complete form of the momentum equation with a less complete momentum equation for dendritic solidification, with isotherms and isoconcentrates that move with a constant velocity.
Abstract: For analyzing dendritic solidification, convection in the mushy zone is based on a momentum equation for a porous medium with a spatially varying fraction of liquid. Results are compared with those obtained with a less complete momentum equation. Calculations are done for directional solidification, with isotherms and isoconcentrates that move with a constant velocity. Thermosolutal convection as a function of time is studied by perturbing the solutal field. The total kinetic energy, the nature of the convection cells, and the isoconcentrates are significantly different for the two models. Hence the complete form of the momentum equation should be used
TL;DR: In this paper, the influence of thermal radiation on natural convection in a participating fluid contained in a square cavity is studied numerically, and the radiative transfer process is solved from the PI approximation.
Abstract: The influence of thermal radiation on natural convection in a participating fluid contained in a square cavity is studied numerically. The radiative transfer process is solved from the PI approximation. The Navier-Stokes equations are solved by a finite difference scheme integrated over control volumes. A numerical study of the so-called window problem (thermally driven cavity) shows the influence of thermal radiation on this reference problem for Rayleigh numbers in the range of 103-107 and Planck numbers varying from 1 to 0.05. The isotherms, streamlines, and heat lines show an increase of the dynamical effects in the central part of the cavity and a significant modification of the boundary layers. Results obtained from the simulation of an isotropically scattering medium are given.
TL;DR: In this paper, the authors present results for three-dimensional laminar and standard K-e turbulent numerical simulations of natural convection cooling of 10 cubic aluminum blocks mounted on an insulated plate, facing a shrouding wall.
Abstract: Results are presented for three-dimensional laminar and standard K-e turbulent numerical simulations of natural convection cooling of 10 cubic aluminum blocks mounted on an insulated plate, facing a shrouding wall. This geometry is chosen so that comparison with experimental results is possible. The problem considered is of great practical importance because it simulates the case of heated electronic chips, mounted on printed board assemblies, which are frequently encountered in electronic industry applications. The problem is mathematically modeled by the three-dimensional conservation differential equations of mass, momentum, energy and turbulent kinetic energy, and dissipation (for the turbulent flow model). These equations are solved numerically by a finite volume method, and the laminar and turbulent results are compared with the experimental results obtained with similar parameters.
TL;DR: For the purpose of fire safety, concrete walls with different thicknesses exposed to the fire course described by ASTM E119 and the following decay stage specified in ISO 834 standard are considere...
Abstract: For the purpose of fire safety, concrete walls with different thicknesses exposed to the fire course described by ASTM E119 and the following decay stage specified in ISO 834 standard are considere...
TL;DR: In this article, a multigrid relaxation method is applied to a pressure-based implicit procedure to solve unseady, incompressible Navier-Stokes equations and the results are compared with single grid results using the OrthoMin conjugate gradient method.
Abstract: A multigrid relaxation method is applied to a pressure-based implicit procedure to solve unseady, incompressible Navier-Stokes equations. The present multigrid method is a Correction Scheme according to Brandt. This method is used to solve the scalar matrices resulting from the finite-volume formulation and uses flux averaging as the restriction operator. The accuracy and computational efficiency are demonstrated with a steady state driven cavity flow and an unsteady flow over a circular cylinder case. The results are compared with single grid results using the OrthoMin conjugate gradient method and experimental data.
TL;DR: In this paper, an alternating direction implicit (ADI) algorithm was used to solve the momentum and energy equations of an internally finned tube of finite thermal conductivity, and the solutions were obtained under the condition of constant flow rate regardless of fin configuration.
Abstract: Numerical solutions of the developing temperature field were obtained for fully developed laminar, incompressible flow in an internally finned tube of finite thermal conductivity. The momentum and energy equations were solved using an alternating direction implicit (ADI) algorithm. First, the laminar flow field was computed for a given fin configuration, and then the temperature fields in the fluid and the solid were solved simultaneously. Two different boundary conditions were considered: fixed temperature, and constant heat flux on the outer tube rim. The solutions were obtained under the condition of constant flow rate, regardless of fin configuration. This feature enabled us to make comparisons among the various cases. The numerical results show that the height and thickness of the fins, thickness of the tube wall, and ratio of the solid to fluid thermal conductivity have pronounced effects on the solution. It is also shown that the assumption of infinite thermal conductivity of the fin is not justifi...
TL;DR: The conjugate mixed convection and conduction transport that arises due to the continuous movement of a heated plate has been numerically investigated in this paper, where the temperature distribution in the solid, as well as in the flow, along with the associated velocity field, need to be studied in detail.
Abstract: The conjugate mixed convection and conduction transport that arises due to the continuous movement of a heated plate has been numerically investigated. The temperature distribution in the solid, as well as in the flow, along with Ike associated velocity field, need to be studied in detail. A numerical study is carried out, assuming a two-dimensional, transient circumstance. The governing elliptic equations are solved, employing finite difference techniques. The transient effects in heat transfer from the plate are studied for the heated plate moving horizontally as well as vertically. The steady state results are obtained for various values of the governing dimensionless parameters, such as the ratio of the thermal conductivity of the fluid Kr to that of the material Ks the Peclet number Pe, Prandtl number Pr, Grashof number Gr, and Reynolds number Re.
TL;DR: In this paper, an annular configuration for which the jet is discharged from a circular tube and, after impingement, is redirected 180° to exit through a annular passage is considered.
Abstract: Axisymmetric, laminar jet impingement cooling of a circular heat source has been simulated under conditions for which discharge of the spent fluid may influence heat transfer from the source. The simulation specifically addresses an annular configuration for which the jet is discharged from a circular tube and, after impingement, is redirected 180° to exit through an annular passage. The flow is strongly influenced by two recirculation zones located adjacent to the jet and in the corner formed by intersection of the outer wall of the annulus with the heater/substrate surface. For jet velocity profiles that are parabolic or uniform, respectively, the radial distribution of the local Nusselt number is characterized by a local maximum or minimum at the stagnation point. If the outer wall of the annulus intersects the outer edge of the heater, the Nusselt number exhibits a local maximum near the edge, irrespective of the jet velocity profile. Parametric calculations have been performed to assess the effects o...
TL;DR: In this article, the simulation of forced convection in convergent and divergent ducts of rectangular cross section is described, and the authors show that the pressure drop decreases, while Nusselt number increases, with increasing Reynolds number or increasing aspect ratio.
Abstract: This paper describes the simulation of forced convection in convergent and divergent ducts of rectangular cross section. The flow is modeled as being three-dimensional and parabolic, with constant wall temperature. The results show that the pressure drop decreases, while Nusselt number increases, with increasing Reynolds number or increasing aspect ratio. For convergent flows, both pressure drop and Nusselt number increase with convergent angle. For divergent flows, pressure drop may decrease with increasing divergent angle due to the recovery of the static pressure from dynamic pressure, but the variation of local Nusselt number is not so great as that of the convergent duct except in the entrance region.
TL;DR: In this article, a stream function-vorticity-temperature formulation is employed in conjunction with body-fitted coordinates for mapping the irregular shape of the timewise changing solid-liquid interface.
Abstract: Transient heat transfer and fluid flow driven by combined buoyancy and surface tension forces during melting of a metal from an isothermal vertical wall are modeled using an implicit moving grid technique. A stream function-vorticity-temperature formulation is employed in conjunction with body-fitted coordinates for mapping the irregular shape of the timewise changing solid-liquid interface. Results show that for augmenting buoyancy and surface tension forces, enhanced fluid velocities, heat transfer, and melting rates occur near the free surface. In contrast, for counteracting buoyancy and surface tension forces, heat transfer and melting rates near the free surface are reduced. The effect of these forces on the overall melting rate is, however, moderate for the Rayleigh (1.15 × 104) and Marangoni (0.0, −3.675 × 103, and 2.1 × 103) numbers considered.
TL;DR: In this article, the hyperbolic Stefan problem with an applied surface heat flux and temperature-dependent thermal conductivity is solved numerically for a semi-infinite slab using Mac-Cormack's predictor-corrector method.
Abstract: The hyperbolic Stefan problem with an applied surface heat flux and temperature-dependent thermal conductivity is solved numerically for a semi-infinite slab using Mac-Cormack's predictor-corrector method. Solutions are presented for cases where the melt temperature is both below and above the instantaneous jump in surface temperature at time t = O+. The interface condition, surface temperature, and internal temperatures are presented for different Stefan numbers and melt temperatures, as well as thermal conductivity both increasing and decreasing with temperature. The results obtained from the hyperbolic solution are compared with those obtained from the parabolic solution.